Deep within an ancient woodland sanctuary, Emek, Luna, and Nova discovered a series of stone gates guarded by fraction puzzles. Each gate required adding, subtracting, multiplying, or dividing fractions, but the friends also had to decide whether each answer was reasonable before the gate would open. They estimated results, checked their calculations, and corrected mistakes when an answer did not make sense. Their careful reasoning unlocked the final passage, revealing a hidden nature archive and helping preserve the sanctuary's secrets.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Use a common denominator of 12 and compare the result with 1.
At one stone gate, Luna estimated that \(\frac{5}{6}+\frac{1}{12}\) should be a little less than 1. Which exact answer matches her estimate?
\(\frac{3}{4}\)\(\frac{11}{12}\)\(\frac{13}{12}\)\(\frac{5}{18}\)Correct! \(\frac{5}{6}+\frac{1}{12}=\frac{10}{12}+\frac{1}{12}=\frac{11}{12}\), which is just less than 1.
Try again. Rewrite \(\frac{5}{6}\) with denominator 12 before adding.
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Hint
Multiply first, then simplify the fraction.
Nova solved \(\frac{4}{9}\times\frac{3}{8}\). What is the numerator of the simplified product?
Correct! The simplified product is \(\frac{1}{6}\).
Try again. Simplify the product after multiplying.
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Hint
Divide by multiplying by the reciprocal, then decide whether the result is reasonable.
A gate shows \(\frac{2}{3}\div\frac{4}{9}\). A student says the answer is \(\frac{1}{6}\). Based on careful reasoning, what should Emek, Luna, and Nova conclude?
The student is correct because division always makes fractions smaller.The student is incorrect because \(\frac{2}{3}\div\frac{4}{9}=\frac{3}{2}\).The student is incorrect because the answer is \(\frac{2}{27}\).The student is correct because \(\frac{2}{3}-\frac{4}{9}=\frac{1}{6}\).Correct! \(\frac{2}{3}\times\frac{9}{4}=\frac{18}{12}=\frac{3}{2}\), which is reasonable because dividing by a fraction less than 1 gives a larger result.
Try again. Multiply by the reciprocal and check whether the answer should be greater than or less than the original fraction.
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